#!/usr/bin/env python
#
# bdalg_test.py - test suite for block diagram algebra
# RMM, 30 Mar 2011 (based on TestBDAlg from v0.4a)

import unittest
import numpy as np
from numpy import sort
import control as ctrl
from control.xferfcn import TransferFunction
from control.statesp import StateSpace
from control.bdalg import feedback
from control.lti import zero, pole

class TestFeedback(unittest.TestCase):
    """These are tests for the feedback function in bdalg.py.  Currently, some
    of the tests are not implemented, or are not working properly.  TODO: these
    need to be fixed."""

    def setUp(self):
        """This contains some random LTI systems and scalars for testing."""

        # Two random SISO systems.
        self.sys1 = TransferFunction([1, 2], [1, 2, 3])
        self.sys2 = StateSpace([[1., 4.], [3., 2.]], [[1.], [-4.]],
            [[1., 0.]], [[0.]])
        # Two random scalars.
        self.x1 = 2.5
        self.x2 = -3.

    def testScalarScalar(self):
        """Scalar system with scalar feedback block."""

        ans1 = feedback(self.x1, self.x2)
        ans2 = feedback(self.x1, self.x2, 1.)

        self.assertAlmostEqual(ans1.num[0][0][0] / ans1.den[0][0][0],
            -2.5 / 6.5)
        self.assertAlmostEqual(ans2.num[0][0][0] / ans2.den[0][0][0], 2.5 / 8.5)

    def testScalarSS(self):
        """Scalar system with state space feedback block."""

        ans1 = feedback(self.x1, self.sys2)
        ans2 = feedback(self.x1, self.sys2, 1.)

        np.testing.assert_array_almost_equal(ans1.A, [[-1.5, 4.], [13., 2.]])
        np.testing.assert_array_almost_equal(ans1.B, [[2.5], [-10.]])
        np.testing.assert_array_almost_equal(ans1.C, [[-2.5, 0.]])
        np.testing.assert_array_almost_equal(ans1.D, [[2.5]])
        np.testing.assert_array_almost_equal(ans2.A, [[3.5, 4.], [-7., 2.]])
        np.testing.assert_array_almost_equal(ans2.B, [[2.5], [-10.]])
        np.testing.assert_array_almost_equal(ans2.C, [[2.5, 0.]])
        np.testing.assert_array_almost_equal(ans2.D, [[2.5]])

        # Make sure default arugments work as well
        ans3 = feedback(self.sys2, 1)
        ans4 = feedback(self.sys2)
        np.testing.assert_array_almost_equal(ans3.A, ans4.A)
        np.testing.assert_array_almost_equal(ans3.B, ans4.B)
        np.testing.assert_array_almost_equal(ans3.C, ans4.C)
        np.testing.assert_array_almost_equal(ans3.D, ans4.D)

    def testScalarTF(self):
        """Scalar system with transfer function feedback block."""

        ans1 = feedback(self.x1, self.sys1)
        ans2 = feedback(self.x1, self.sys1, 1.)

        np.testing.assert_array_almost_equal(ans1.num, [[[2.5, 5., 7.5]]])
        np.testing.assert_array_almost_equal(ans1.den, [[[1., 4.5, 8.]]])
        np.testing.assert_array_almost_equal(ans2.num, [[[2.5, 5., 7.5]]])
        np.testing.assert_array_almost_equal(ans2.den, [[[1., -0.5, -2.]]])

        # Make sure default arugments work as well
        ans3 = feedback(self.sys1, 1)
        ans4 = feedback(self.sys1)
        np.testing.assert_array_almost_equal(ans3.num, ans4.num)
        np.testing.assert_array_almost_equal(ans3.den, ans4.den)

    def testSSScalar(self):
        """State space system with scalar feedback block."""

        ans1 = feedback(self.sys2, self.x1)
        ans2 = feedback(self.sys2, self.x1, 1.)

        np.testing.assert_array_almost_equal(ans1.A, [[-1.5, 4.], [13., 2.]])
        np.testing.assert_array_almost_equal(ans1.B, [[1.], [-4.]])
        np.testing.assert_array_almost_equal(ans1.C, [[1., 0.]])
        np.testing.assert_array_almost_equal(ans1.D, [[0.]])
        np.testing.assert_array_almost_equal(ans2.A, [[3.5, 4.], [-7., 2.]])
        np.testing.assert_array_almost_equal(ans2.B, [[1.], [-4.]])
        np.testing.assert_array_almost_equal(ans2.C, [[1., 0.]])
        np.testing.assert_array_almost_equal(ans2.D, [[0.]])

    def testSSSS1(self):
        """State space system with state space feedback block."""

        ans1 = feedback(self.sys2, self.sys2)
        ans2 = feedback(self.sys2, self.sys2, 1.)

        np.testing.assert_array_almost_equal(ans1.A, [[1., 4., -1., 0.],
            [3., 2., 4., 0.], [1., 0., 1., 4.], [-4., 0., 3., 2]])
        np.testing.assert_array_almost_equal(ans1.B, [[1.], [-4.], [0.], [0.]])
        np.testing.assert_array_almost_equal(ans1.C, [[1., 0., 0., 0.]])
        np.testing.assert_array_almost_equal(ans1.D, [[0.]])
        np.testing.assert_array_almost_equal(ans2.A, [[1., 4., 1., 0.],
            [3., 2., -4., 0.], [1., 0., 1., 4.], [-4., 0., 3., 2.]])
        np.testing.assert_array_almost_equal(ans2.B, [[1.], [-4.], [0.], [0.]])
        np.testing.assert_array_almost_equal(ans2.C, [[1., 0., 0., 0.]])
        np.testing.assert_array_almost_equal(ans2.D, [[0.]])

    def testSSSS2(self):
        """State space system with state space feedback block, including a
        direct feedthrough term."""

        sys3 = StateSpace([[-1., 4.], [2., -3]], [[2.], [3.]], [[-3., 1.]],
            [[-2.]])
        sys4 = StateSpace([[-3., -2.], [1., 4.]], [[-2.], [-6.]], [[2., -3.]],
            [[3.]])

        ans1 = feedback(sys3, sys4)
        ans2 = feedback(sys3, sys4, 1.)

        np.testing.assert_array_almost_equal(ans1.A,
            [[-4.6, 5.2, 0.8, -1.2], [-3.4, -1.2, 1.2, -1.8],
             [-1.2, 0.4, -1.4, -4.4], [-3.6, 1.2, 5.8, -3.2]])
        np.testing.assert_array_almost_equal(ans1.B,
            [[-0.4], [-0.6], [-0.8], [-2.4]])
        np.testing.assert_array_almost_equal(ans1.C, [[0.6, -0.2, -0.8, 1.2]])
        np.testing.assert_array_almost_equal(ans1.D, [[0.4]])
        np.testing.assert_array_almost_equal(ans2.A,
            [[-3.57142857142857, 4.85714285714286, 0.571428571428571,
                -0.857142857142857],
             [-1.85714285714286, -1.71428571428571, 0.857142857142857,
                -1.28571428571429],
             [0.857142857142857, -0.285714285714286, -1.85714285714286,
                -3.71428571428571],
             [2.57142857142857, -0.857142857142857, 4.42857142857143,
                -1.14285714285714]])
        np.testing.assert_array_almost_equal(ans2.B, [[0.285714285714286],
            [0.428571428571429], [0.571428571428571], [1.71428571428571]])
        np.testing.assert_array_almost_equal(ans2.C, [[-0.428571428571429,
            0.142857142857143, -0.571428571428571, 0.857142857142857]])
        np.testing.assert_array_almost_equal(ans2.D, [[-0.285714285714286]])


    def testSSTF(self):
        """State space system with transfer function feedback block."""

        # This functionality is not implemented yet.
        pass

    def testTFScalar(self):
        """Transfer function system with scalar feedback block."""

        ans1 = feedback(self.sys1, self.x1)
        ans2 = feedback(self.sys1, self.x1, 1.)

        np.testing.assert_array_almost_equal(ans1.num, [[[1., 2.]]])
        np.testing.assert_array_almost_equal(ans1.den, [[[1., 4.5, 8.]]])
        np.testing.assert_array_almost_equal(ans2.num, [[[1., 2.]]])
        np.testing.assert_array_almost_equal(ans2.den, [[[1., -0.5, -2.]]])

    def testTFSS(self):
        """Transfer function system with state space feedback block."""

        # This functionality is not implemented yet.
        pass

    def testTFTF(self):
        """Transfer function system with transfer function feedback block."""

        ans1 = feedback(self.sys1, self.sys1)
        ans2 = feedback(self.sys1, self.sys1, 1.)

        np.testing.assert_array_almost_equal(ans1.num, [[[1., 4., 7., 6.]]])
        np.testing.assert_array_almost_equal(ans1.den,
            [[[1., 4., 11., 16., 13.]]])
        np.testing.assert_array_almost_equal(ans2.num, [[[1., 4., 7., 6.]]])
        np.testing.assert_array_almost_equal(ans2.den, [[[1., 4., 9., 8., 5.]]])

    def testLists(self):
        """Make sure that lists of various lengths work for operations"""
        sys1 = ctrl.tf([1, 1], [1, 2])
        sys2 = ctrl.tf([1, 3], [1, 4])
        sys3 = ctrl.tf([1, 5], [1, 6])
        sys4 = ctrl.tf([1, 7], [1, 8])
        sys5 = ctrl.tf([1, 9], [1, 0])

        # Series
        sys1_2 = ctrl.series(sys1, sys2)
        np.testing.assert_array_almost_equal(sort(pole(sys1_2)), [-4., -2.])
        np.testing.assert_array_almost_equal(sort(zero(sys1_2)), [-3., -1.])
        
        sys1_3 = ctrl.series(sys1, sys2, sys3);
        np.testing.assert_array_almost_equal(sort(pole(sys1_3)),
                                             [-6., -4., -2.])
        np.testing.assert_array_almost_equal(sort(zero(sys1_3)), 
                                             [-5., -3., -1.])
        
        sys1_4 = ctrl.series(sys1, sys2, sys3, sys4);
        np.testing.assert_array_almost_equal(sort(pole(sys1_4)),
                                             [-8., -6., -4., -2.])
        np.testing.assert_array_almost_equal(sort(zero(sys1_4)),
                                             [-7., -5., -3., -1.])
        
        sys1_5 = ctrl.series(sys1, sys2, sys3, sys4, sys5);
        np.testing.assert_array_almost_equal(sort(pole(sys1_5)),
                                             [-8., -6., -4., -2., -0.])
        np.testing.assert_array_almost_equal(sort(zero(sys1_5)), 
                                             [-9., -7., -5., -3., -1.])

        # Parallel 
        sys1_2 = ctrl.parallel(sys1, sys2)
        np.testing.assert_array_almost_equal(sort(pole(sys1_2)), [-4., -2.])
        np.testing.assert_array_almost_equal(sort(zero(sys1_2)),
                                             sort(zero(sys1 + sys2)))
        
        sys1_3 = ctrl.parallel(sys1, sys2, sys3);
        np.testing.assert_array_almost_equal(sort(pole(sys1_3)),
                                             [-6., -4., -2.])
        np.testing.assert_array_almost_equal(sort(zero(sys1_3)), 
                                             sort(zero(sys1 + sys2 + sys3)))
        
        sys1_4 = ctrl.parallel(sys1, sys2, sys3, sys4);
        np.testing.assert_array_almost_equal(sort(pole(sys1_4)),
                                             [-8., -6., -4., -2.])
        np.testing.assert_array_almost_equal(sort(zero(sys1_4)), 
                                             sort(zero(sys1 + sys2 + 
                                                       sys3 + sys4)))

        
        sys1_5 = ctrl.parallel(sys1, sys2, sys3, sys4, sys5);
        np.testing.assert_array_almost_equal(sort(pole(sys1_5)),
                                             [-8., -6., -4., -2., -0.])
        np.testing.assert_array_almost_equal(sort(zero(sys1_5)), 
                                             sort(zero(sys1 + sys2 + 
                                                       sys3 + sys4 + sys5)))
    def testMimoSeries(self):
        """regression: bdalg.series reverses order of arguments"""
        g1 = ctrl.ss([],[],[],[[1,2],[0,3]])
        g2 = ctrl.ss([],[],[],[[1,0],[2,3]])
        ref = g2*g1
        tst = ctrl.series(g1,g2)
        # assert_array_equal on mismatched matrices gives
        # "repr failed for <matrix>: ..."
        def assert_equal(x,y):
            np.testing.assert_array_equal(np.asarray(x),
                                          np.asarray(y))
        assert_equal(ref.A, tst.A)
        assert_equal(ref.B, tst.B)
        assert_equal(ref.C, tst.C)
        assert_equal(ref.D, tst.D)

    def test_feedback_args(self):
        # Added 25 May 2019 to cover missing exception handling in feedback()
        # If first argument is not LTI or convertable, generate an exception
        args = ([1], self.sys2)
        self.assertRaises(TypeError, ctrl.feedback, *args)

        # If second argument is not LTI or convertable, generate an exception
        args = (self.sys1, np.array([1]))
        self.assertRaises(TypeError, ctrl.feedback, *args)

        # Convert first argument to FRD, if needed
        h = TransferFunction([1], [1, 2, 2])
        omega = np.logspace(-1, 2, 10)
        frd = ctrl.FRD(h, omega)
        sys = ctrl.feedback(1, frd)
        self.assertTrue(isinstance(sys, ctrl.FRD))


if __name__ == "__main__":
    unittest.main()
